Bayesian loss-based approach to change point analysis

A loss-based approach to change point analysis is proposed. In particular, the problem is looked from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The second contribution aims to estimate the number of change points by using a loss-based approach recently introduced in the literature. The latter considers change point estimation as a model selection exercise. The performance of the proposed approach is shown on simulated data and real data sets.

[1]  J. Hartigan,et al.  Product Partition Models for Change Point Problems , 1992 .

[2]  S. Walker,et al.  An Objective Bayesian Criterion to Determine Model Prior Probabilities , 2015 .

[3]  Florent Chatelain,et al.  Bayesian Model for Multiple Change-Points Detection in Multivariate Time Series , 2014, IEEE Transactions on Signal Processing.

[4]  Philippe Naveau,et al.  Bayesian multiple change points and segmentation: Application to homogenization of climatic series , 2009 .

[5]  J. Hartigan,et al.  A Bayesian Analysis for Change Point Problems , 1993 .

[6]  James O. Berger,et al.  Objective Priors for Discrete Parameter Spaces , 2012 .

[7]  S. Robin,et al.  Exact Bayesian inference for off-line change-point detection in tree-structured graphical models , 2016, Stat. Comput..

[8]  Objective Bayesian analysis of SAR models , 2013 .

[9]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[10]  Eric Moulines,et al.  Adaptive sequential Monte Carlo by means of mixture of experts , 2011, Stat. Comput..

[11]  Gary Koop,et al.  Prior Elicitation in Multiple Change-Point Models , 2004 .

[12]  J. Berger,et al.  The Intrinsic Bayes Factor for Model Selection and Prediction , 1996 .

[13]  Ramsés H. Mena,et al.  On a Nonparametric Change Point Detection Model in Markovian Regimes , 2014 .

[14]  A. Raftery,et al.  Bayesian analysis of a Poisson process with a change-point , 1986 .

[15]  S. Walker,et al.  An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces , 2015 .

[16]  Adrian F. M. Smith,et al.  Hierarchical Bayesian Analysis of Changepoint Problems , 1992 .

[17]  Haipeng Xing,et al.  A SIMPLE BAYESIAN APPROACH TO MULTIPLE CHANGE-POINTS , 2011 .

[18]  Marco Scarsini,et al.  Change-point problems: a Bayesian nonparametric approach , 1985 .

[19]  Nicholas A. Heard,et al.  Adaptive Sequential Monte Carlo for Multiple Changepoint Analysis , 2015 .

[20]  Chandra Erdman,et al.  bcp: An R Package for Performing a Bayesian Analysis of Change Point Problems , 2007 .

[21]  Rosangela Helena Loschi,et al.  Extension to the product partition model: computing the probability of a change , 2005, Comput. Stat. Data Anal..

[22]  A. F. Smith.  A Bayesian approach to inference about a change-point in a sequence of random variables , 1975 .

[23]  George Casella,et al.  An objective Bayesian analysis of the change point problem , 2005 .

[24]  P. Fearnhead,et al.  On‐line inference for multiple changepoint problems , 2007 .

[25]  Jun Yu.  Testing for a finite variance in stock return distributions , 2001 .

[26]  A. Raftery,et al.  A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability , 1997 .

[27]  M. J. Bayarri,et al.  Objective Bayesian Analysis of Multiple Changepoints for Linear Models , 2006 .

[28]  S. Chib.  Estimation and comparison of multiple change-point models , 1998 .

[29]  D. Stephens.  Bayesian Retrospective Multiple‐Changepoint Identification , 1994 .

[30]  Pulak Ghosh,et al.  Dirichlet Process Hidden Markov Multiple Change-point Model , 2015, 1505.01665.

[31]  Antonietta Mira,et al.  Bayesian hierarchical nonparametric inference for change-point problems , 1996 .

[32]  H. Chernoff,et al.  ESTIMATING THE CURRENT MEAN OF A NORMAL DISTRIBUTION WHICH IS SUBJECTED TO CHANGES IN TIME , 1964 .

[33]  Edward I. George,et al.  Dilution priors: Compensating for model space redundancy , 2010 .

[34]  J. N. S. Matthews,et al.  An investigation of changepoints in the annual number of cases of haemolytic uraemic syndrome , 1993 .

[35]  R. Berk,et al.  Limiting Behavior of Posterior Distributions when the Model is Incorrect , 1966 .

[36]  Ming Tan,et al.  Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome , 2009, Comput. Stat. Data Anal..